MiniSlack *is* Slackware. I switched to MiniSlack because it gave me a much smaller system without having to fuss with all the package selections, it comes with Firefox (ahem, Patrick, I've been asking for this for a year and a half) and a bunch of other, useful stuff, and tries to keep to ONE app for each task. Also, it works with the Slack 10.1 slapt-get repositories (and comes with it installed, even). It works with Webmin for Slack 10.1. All 10.1 packages I tried worked.

In short, this is just a "mini" version of Slackware (thus the name). If you like Slack but want a sleeker but fully compatible version, try MiniSlack. I'm running my home webserver on it right now.